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Popular >

derivative of xcos(x)sin(x)

Solution

derivative of

x cos (x) sin (x)

Solution

cos (x) sin (x) + x cos (2 x)

Solution steps

\frac{d}{d x} (x cos (x) sin (x))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = cos (x) sin (x)

= \frac{d x}{d x} cos (x) sin (x) + \frac{d}{d x} (cos (x) sin (x)) x

\frac{d x}{d x} = 1

\frac{d}{d x} (cos (x) sin (x)) = cos (2 x)

= 1 \cdot cos (x) sin (x) + cos (2 x) x

Simplify

= cos (x) sin (x) + x cos (2 x)

Popular Examples

integral of-2/(1-2x)

\int - \frac{2}{1 - 2 x} d x

integral from 1 to 4 of (x^2+1)/(5x-x^2)

\int_{1}^{4} \frac{x ^{2} + 1}{5 x - x ^{2}} d x

implicit (dy}{dx},\frac{(x^2))/4+y^2=1 implicit derivative

\frac{d y}{d x}, \frac{( x ^{2} )}{4} + y^{2} = 1

derivative of 1/(4x^3)

\frac{d}{d x} (\frac{1}{4 x ^{3}})

derivative of ln(x^3-1)

\frac{d}{d x} (ln (x^{3} - 1))

Frequently Asked Questions (FAQ)

What is the derivative of xcos(x)sin(x) ?
The derivative of xcos(x)sin(x) is cos(x)sin(x)+xcos(2x)
What is the first derivative of xcos(x)sin(x) ?
The first derivative of xcos(x)sin(x) is cos(x)sin(x)+xcos(2x)